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Parallel storage systems distribute data onto several devices. This allows high access bandwidth that is needed for parallel computing systems. It also improves the storage reliability, provided erasure-tolerant coding is applied and the coding is fast enough. In this paper we assume storage systems that apply data distribution and coding in a combined way. We describe, how coding can be done parallel on multicore and GPU systems in order to keep track with the high storage access bandwidth. A framework is introduced that calculates coding equations from parameters and translates them into OpenMP- and OpenCL-based coding modules. These modules do the encoding for data that is written to the storage system, and do the decoding in case of failures of storage devices. We report on the performance of the coding modules and identify factors that influence the coding performance.